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Q8×C4⋊C4×D67 #31015129

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×C4⋊C4×D67

Splittings

FittingQ8×C4⋊C4×C67 ⋊ C2
SylowC67 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D67
commutatorC22×C67C24×C4
FittingQ8×C4⋊C4×C67C2
socle, cosocleC23×C67C25
prime radicalC23×D67C24
hypercenterQ8×C4⋊C4D67
hypocenterC67C2×Q8×C4⋊C4
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 328866);